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A runner, jogging along a straight line path, starts at a position $60 \mathrm{m}$ east of a milestone marker and heads west. After a short time interval he is \(20 \mathrm{m}\) west of the mile marker. Choose east to be the positive \(x\) -direction. (a) What is the runner's displacement from his starting point? (b) What is his displacement from the milestone? (c) The runner then turns around and heads east. If at a later time the runner is \(140 \mathrm{m}\) east of the milestone, what is his displacement from the starting point at this time? (d) What is the total distance traveled from the starting point if the runner stops at the final position listed in part (c)?

At 3 P.M. a car is located \(20 \mathrm{km}\) south of its starting point. One hour later it is \(96 \mathrm{km}\) farther south. After two more hours, it is \(12 \mathrm{km}\) south of the original starting point. (a) What is the displacement of the car between 3 P.M. and 6 P.M.? (b) What is the displacement of the car from the starting point to the location at 4 P.M.? (c) What is the displacement of the car between 4 P.M. and 6 P.M.?

A ball thrown by a pitcher on a women's softball team is timed at 65.0 mph. The distance from the pitching rubber to home plate is \(43.0 \mathrm{ft}\). In major league baseball the corresponding distance is \(60.5 \mathrm{ft}\). If the batter in the softball game and the batter in the baseball game are to have equal times to react to the pitch, with what speed must the baseball be thrown? Assume the ball travels with a constant velocity. [Hint: There is no need to convert units; set up a ratio.]

A relay race is run along a straight-line track of length \(300.0 \mathrm{m}\) running south to north. The first runner starts at the south end of the track and passes the baton to a teammate at the north end of the track. The second runner races back to the start line and passes the baton to a third runner who races \(100.0 \mathrm{m}\) northward to the finish line. The magnitudes of the average velocities of the first, second, and third runners during their parts of the race are \(7.30 \mathrm{m} / \mathrm{s}, 7.20 \mathrm{m} / \mathrm{s}\) and \(7.80 \mathrm{m} / \mathrm{s},\) respectively. What is the average velocity of the baton for the entire race? [Hint: You will need to find the time spent by each runner in completing her portion of the race.]

The St. Charles streetcar in New Orleans starts from rest and has a constant acceleration of \(1.20 \mathrm{m} / \mathrm{s}^{2}\) for \(12.0 \mathrm{s} .\) (a) Draw a graph of \(v_{x}\) versus \(t .\) (b) How far has the train traveled at the end of the \(12.0 \mathrm{s} ?\) (c) What is the speed of the train at the end of the \(12.0 \mathrm{s} ?\) (d) Draw a motion diagram, showing the streetcar's position at \(2.0-\mathrm{s}\) intervals.

An airplane lands and starts down the runway with a southwest velocity of $55 \mathrm{m} / \mathrm{s}$. What constant acceleration allows it to come to a stop in \(1.0 \mathrm{km} ?\)

A train is traveling south at \(24.0 \mathrm{m} / \mathrm{s}\) when the brakes are applied. It slows down with a constant acceleration to a speed of $6.00 \mathrm{m} / \mathrm{s}\( in a time of \)9.00 \mathrm{s} .$ (a) Draw a graph of \(v_{x}\) versus \(t\) for a 12 -s interval (starting \(2 \mathrm{s}\) before the brakes are applied and ending 1 s after the brakes are released). Let the \(x\) -axis point to the north. (b) What is the acceleration of the train during the \(9.00-\mathrm{s}\) interval? \((\mathrm{c})\) How far does the train travel during the $9.00 \mathrm{s} ?$

A car is speeding up and has an instantaneous velocity of $1.0 \mathrm{m} / \mathrm{s}\( in the \)+x\( -direction when a stopwatch reads \)10.0 \mathrm{s} .$ It has a constant acceleration of \(2.0 \mathrm{m} / \mathrm{s}^{2}\) in the \(+x\) -direction. (a) What change in speed occurs between \(t=10.0 \mathrm{s}\) and \(t=12.0 \mathrm{s} ?(\mathrm{b})\) What is the speed when the stopwatch reads \(12.0 \mathrm{s} ?\)

A train is traveling along a straight, level track at $26.8 \mathrm{m} / \mathrm{s} \quad(60.0 \mathrm{mi} / \mathrm{h}) .$ Suddenly the engineer sees a truck stalled on the tracks \(184 \mathrm{m}\) ahead. If the maximum possible braking acceleration has magnitude \(1.52 \mathrm{m} / \mathrm{s}^{2},\) can the train be stopped in time?

please assume the free-fall acceleration \(g=9.80 \mathrm{m} / \mathrm{s}^{2}\) unless a more precise value is given in the problem statement. Ignore air resistance. A penny is dropped from the observation deck of the Empire State building (369 m above ground). With what velocity does it strike the ground?